The BIPM Joint Committee for Guides in Metrology (JCGM) has the responsibility for the following two documents:

a) Guide to Expression of Uncertainty in Measurement (known as the GUM) and

b) International Vocabulary of Metrology - Basics and General Concepts and Associated Terms (known as the VIM)

The JCGM-WG1 has recently completed its first supplement to the GUM and a revised edition of the VIM, prepared by JCGM-WG2, are now both available on the BIPM website.

We recommend that readers use these two documents as the definitive source for uncertainty calculations and statements and for general metrology vocabulary.

The full copy of the GUM is available on the ISO website and a free copy of the VIM on the BIPM website.

The definitions below are an extract from the VIM and are placed here for convenience.

Property of a phenomenon , body, or substance, to which a number can be assigned with respect to a reference.

It is a scalar quantity, defined and adopted by convention, with which any other quantity of the same kind can be compared to express the ratio of the two quantities as a number.

Measurement unit for a derived quantity.
Examples
The metre per second , symbol m/s, and the centimeter per second, symbol cm/s, are derived units of speed in the SI. The kilometre per hour, symbol km/h, is a unit of speed outside the SI but accepted for use with the SI. The knot, equal to one nautical mile per hour, is a unit of speed outside the SI.

Coherent system of units based on the International System of Quantities, their names and symbols, and a series of prefixes and their names and symbols, together with rules for their use, adopted by the General Conference on Weights and Measures (CGPM). The SI is founded on the seven base quantities of the ISO and the base units contained in the following table.

Number and reference together expressing magnitude of a quantity Examples
a) Length of given rod 5.34 m or 534 cm
b) Mass of a given body 0.152 kg of 152 g
c) Celcius temperature of
a given sample -5º C
d) refractive index of given 1.32 sample of glass

Process of experimentally obtaining one or more quantity that can reasonably be attributed to quantity
Measurement implies comparison of quantities or counting of entities
Measurement presupposes description of the quantity commensurate with the intended use of the measurement result, a measurement procedure, and a calibrated measuring system operating according to a specified measurement procedure.

Field of knowledge concerned with measurement

Quantity intended to be measured
The application of a measurand requires description of the state of the phenomenon, body, or substance carrying the quantity, including any relevant component and the chemical entities involved.

Generic description of a logical organization of operations used in a measurement
measurement methods may be qualified in various ways such as:
a) substitution measurement method
b) differential measurement method, and
c) null measurement method
or
d) direct measurement method, and
e) indirect measurement method

Detailed description of a measurement according to one or more measurement principles and to a given measurement method, based on a measurement model and including any calculation to obtain a measurement result.
a) A measurement procedure is usually documented in sufficient detail to enable an operator to perform a measurement.
b) A measurement procedure can include a target measurement uncertainty.
c) A measurement procedure is sometimes called a standard operating procedure, abbreviated SOP.

Measurement procedure accepted as providing measurement results fit for their intended use in assessing measurement trueness quantity values obtained from other measurement procedure for quantities of the same kind, or in characterizing reference materials

Set of quantity values being attributed to a measurand together with any other available relevant information
a) A measurement generally provides information about the set of quantity values, such that some may be more representative of the measurand than others.This may be
demonstrated in the form of a probability density function (PDF).
b) A measurement result is generally expressed as a single measured quantity value
and a measurement uncertainty. If the measurement uncertainty is considered to be
negligible for some purpose, the measurement result may be expressed as a
single measured quantity value. In many fields this is the common way of expressing
a measurement result.

Quantity value representing a measurement result

Quantity value consistent with the definition of a quantity

Quantity value attributed by agreement to a quantity for a given purpose
Examples
a) standard acceleration of free fall (formerly called standard acceleration due to gravity) is g= 9.80665 m s-2
b) the conventional quantity value of the Josephson constant, Kj-90=483597.9 GHz V-1
c) the conventional quantity value of a given mass standard, m=100.00347 g.

Closeness of agreement between a measured quantity value and a true quantity value of the measurand

Closeness of agreement between the average of an infinite number of replicate measured quantity values and a reference quantity value
Notes
A reference quantity value can be a true quantity value of the measurand or an assigned quantity value of a measurement standard with negligible measurement uncertainty.
The term “measurement trueness” should not be used for ‘measurement accuracy’ and vice versa.

Closeness of agreement between indications obtained by replicate measurements on the same or similar objects under specified conditions
Notes
a) Measurement precision is usually expressed numerically by measures of imprecision,
such as standard deviation, variance, or coefficient of variation under the specified conditions of measurement.
b) The specified conditions can be repeatability conditions of measurement, intermediate
precision conditions of measurement, or reproducibilityconditions of measurement
(see ISO 5725-5:1998).
c) Measurement precision is used to define measurement repeatability, intermediate
measurement precision, and measurement reproducibility.
d) Sometimes “precision” is erroneously used to mean ‘measurement accuracy(b)’

Difference of measured quantity value and reference quantity value
• The sign of the difference must be noted
• Measurement error should not be confused with production error or mistake.

Component of measurement error that in replicate measurements remains constant or varies in a predictable manner

Systematic measurement error or its estimate, with respect to a reference quantity value

Component of measurement error that in replicate measurements varies in an unpredictable manner

Condition of measurement in a set of conditions that includes the same measurement procedure, same operators, same measuring system, same operation conditions and same location, and replicate measurements on the same or similar objects over a short period of time

Measurement precision under a set of repeatability conditions of measurement

Condition of measurement in a set of conditions that includes different locations, operators, measuring systems, and replicate measurements on the same or similar objects

Measurement precision under reproducibility conditions of measurement

Parameter characterizing the dispersion of the quantity values being attributed to a measurand, based on the information used.
Notes
Measurement uncertainty includes components arising from systematic effects, such as components associated with corrections and the assigned quantity values of measurement standards, as well as the definitional uncertainty. Sometimes known systematic effects are not corrected for but are instead treated as uncertainty components.
The parameter may be, for example, a standard deviation called standard measurement uncertainty (or a specified multiple of it), or half width of an interval, having a stated coverage probability.
Measurement uncertainty comprises, in general, many components. Some of these may be evaluated by Type A evaluation of measurement uncertainty from the statistical distribution of the quantity values from series of measurements and can be characterized by experimental standard deviations. The other components, which may be evaluated by Type B evaluation of measurement uncertainty, can also be characterized by standard deviations, evaluated from probability density functions based on experience or other information.

Evaluation of a component of measurement uncertainty by a statistical analysis of quantity values obtained under defined measurement conditions

Evaluation of a component of measurement uncertainty determined by means other than a Type A evaluation of measurement uncertainty
Example
Evaluation based on information
• associated with authoritative published quantity values
• associated with the quantity value of a certified reference material
• obtained from a calibration certificate and incorporation of drift
• obtained from the accuracy class of a verified measuring instrument
• obtained from limits deduced through personal experience

Measurement uncertainty expressed as a standard deviation

Standard measurement uncertainty that is obtained from the measurement results of the input quantities in measurement model

Statement of a measurement uncertainty, of the components of that measurement uncertainty, and of their calculation and combination

Product of a combined standard measurement uncertainty and a factor larger than the number one
Expanded measurement uncertainty is termed “overall uncertainty”
The term ‘factor’ in this definition refers to a coverage factor.

Number larger than one by which a combined standard measurement uncertainty is multiplied to obtain an expanded measurement uncertainty

Operation that, under specified conditions, in a first step establishes a relation between the quantity values with measurement uncertainties provided by measurement standards and corresponding indications with associated measurement uncertainties and, in a second step, uses this information to establish a relation for obtaining a measurement result from an indication

Sequence of calibrations from a stated reference to the final measuring instrument or measuring system, where the outcome of each calibration depends on the outcome of the previous calibration

Property of measurement result whereby the result can be related to a stated reference through a documented unbroken chain of calibrations, each contributing to the measurement uncertainty

Provision of objective evidence that a given item fulfils specified requirements, taking any measurement uncertainty into consideration
Examples
Confirmation that a given reference material as claimed is homogeneous for the quantity and measurement procedure concerned , down to test portion having a mass of 10 mg
Confirmation that stated performance properties or legal requirements of a measuring system are achieved.

Verification, where the specified requirements are adequate for a stated use
Example
A measurement procedure, ordinarily used for the measurement of nitrogen concentration in water may be validated also for the measurement of nitrogen concentration in human serum.

Quantity that must be measured, or a quantity, the value of which can be otherwise obtained in order to calculate a measured quantity value of a measurand
Example
When the length of a rod is being measured, temperature, length, and the linear thermal expansion coefficient of the rod are input quantities in a measurement model.

Quantity, that the measured value of which is calculated using the values of input quantities in a measurement model

Quantity that, in a direct measurement, does not affect the quantity that is actually measured, but affects the relation between the indication and the measurement result

Modification, applied to a measured quantity value, to compensate for a known systematic effect

Device used for making measurements, alone or in conjunction with supplementary device(s)
A measuring instrument alone may be considered to fbe ameasuring system
A measuring instrument may be an indicating measuring instrument or a material measure

Set of one or more measuring instruments and often other devices, including any reagent and supply, assembled and adapted to give measured quantity values within specified intervals for quantities of specified kinds ( a measuring system may consist of only one measuring instrument)

Measuring instrument providing an output signal carrying information about the value of the quantity being measured
For example
Ammeter, micrometer , thermometer, electronic balance

Measuring instrument reproducing or supplying, in a permanent manner during the use, quantities of one or more given kinds, each with an assigned value ( weight piece, volume measure, standard electric resistor, line scale, gauge block, standard signal generator)

Device, used in measurement, that provides an output quantity having a specified relation to the input quantity ( thermocouple, current transformer, strain gauge, pH electrode, Bourden tube, bimetal strip)

Element of a measuring system that is directly affected by the phenomenon, body, or substance carrying the quantity to be measured
Examples
a) Sensing coil of a platinum resistance thermometer
b) rotor of turbine flow meter
c) Bourden tube of a pressure gauge
d) Float of a level-measuring instrument
e) Photocell of a spectrometer
f) Thermotropic liquid crystal which changes color as a function of temperature

Device or substance that indicates the presence of a phenomenon, body, or substance when a threshold value of an associated quantity is exceeded
a) a halogen detector
b) a litmus paper

Performanceevaluation condition of use prescribed for evaluation the performance of a measuring instrument or measuring system or for comparison of measurement results

Quotient of the change in the indication and the corresponding change in the value of the quantity being measured

Largest change in the value of a quantity being measured that causes no detectable change in the corresponding indication

Ability of a measuring instrument or measuring system to maintain its metrological properties constant with time

Continuous change in an indication, related neither to a change in the quantity being measured nor to a change of any recognized influence quantity

Component of measurement uncertainty arising from the measuring instrument of measuring system in use, and obtained by its calibration

Extreme value of the measurement error, with respect to a known reference quantity value, permitted by specifications or regulations for a given measurement, measuring instrument, or measuring system

Realization of the definition of a given quantity, with stated quantity value and measurement uncertainty, used as a reference
Example
a) 1 kg mass standard
b) 100 ohm standard resistor
c) Cesium frequency standard
d) Reference material

Measurement standard recognized by signatories to an international agreement and intended to serve worldwide

Measurement standard recognized by national authority to serve in the country

Measurement standard whose quantity value and measurement uncertainty are established using a primary procedure

Measurement standard whose quantity value and measurement uncertainty are assigned though calibration with respect to a primary measurement standard for a quantity of the same kind

Measurement standard designated for the calibration of working measurement standards for quantities of a given kind in a given organization or at a given location

Measurement standard that is used routinely to calibrate or verify measuring instruments or measuring systems

Measurement standard , sometimes of special construction, intended for transport between different locations